Actual Path

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Jian-yang Zhu - One of the best experts on this subject based on the ideXlab platform.

  • Two-dimensional small-world networks: navigation with local information.
    Physical review. E Statistical nonlinear and soft matter physics, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability , each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance away decays as r(-a). Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For alpha < 3 and alpha not equal to 2, a scaling relation is found between the average Actual Path length and , where is the average length of the additional long range links. Given pL > 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough is obtained. At alpha = 2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For alpha > 3, the average Actual Path length is nearly linear with network size.

  • Two-dimensional small-world networks: navigation with local information.
    Physical Review E, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup -{alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha} 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At {alpha}=2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For {alpha}>3, the average Actual Path length is nearly linear with network size.

Jian-zhen Chen - One of the best experts on this subject based on the ideXlab platform.

  • Two-dimensional small-world networks: navigation with local information.
    Physical review. E Statistical nonlinear and soft matter physics, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability , each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance away decays as r(-a). Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For alpha < 3 and alpha not equal to 2, a scaling relation is found between the average Actual Path length and , where is the average length of the additional long range links. Given pL > 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough is obtained. At alpha = 2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For alpha > 3, the average Actual Path length is nearly linear with network size.

  • Two-dimensional small-world networks: navigation with local information.
    Physical Review E, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup -{alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha} 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At {alpha}=2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For {alpha}>3, the average Actual Path length is nearly linear with network size.

Wei Liu - One of the best experts on this subject based on the ideXlab platform.

  • Two-dimensional small-world networks: navigation with local information.
    Physical review. E Statistical nonlinear and soft matter physics, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability , each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance away decays as r(-a). Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For alpha < 3 and alpha not equal to 2, a scaling relation is found between the average Actual Path length and , where is the average length of the additional long range links. Given pL > 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough is obtained. At alpha = 2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For alpha > 3, the average Actual Path length is nearly linear with network size.

  • Two-dimensional small-world networks: navigation with local information.
    Physical Review E, 2006
    Co-Authors: Jian-zhen Chen, Wei Liu, Jian-yang Zhu
    Abstract:

    A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r{sup -{alpha}}. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For {alpha} 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At {alpha}=2 and 3, this kind of scaling breaks down, and different functions of the average Actual Path length are obtained. For {alpha}>3, the average Actual Path length is nearly linear with network size.

Hawoong Jeong - One of the best experts on this subject based on the ideXlab platform.

  • Path finding strategies in scale-free networks
    Physical Review E, 2002
    Co-Authors: Beom Jun Kim, Chang No Yoon, Seung Kee Han, Hawoong Jeong
    Abstract:

    Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556We numerically investigate the scale-free network model of Barab´asi and Albert [A. L. Barab´asiand R. Albert, Science 286, 509 (1999)] through the use of various Path finding strategies. In realnetworks, global network information is not accessible to each vertex, and the Actual Path connectingtwo vertices can sometimes be much longer than the shortest one. A generalized diameter dependingon the Actual Path finding strategy is introduced, and a simple strategy, which utilizes only localinformation on the connectivity, is suggested and shown to yield small-world behavior: the diameterD of the network increases logarithmically with the network size N, the same as is found with globalstrategy. If Paths are sought at random, D ∼ N

  • Path finding strategies in scale-free networks.
    Physical review. E Statistical nonlinear and soft matter physics, 2002
    Co-Authors: Beom Jun Kim, Chang No Yoon, Seung Kee Han, Hawoong Jeong
    Abstract:

    We numerically investigate the scale-free network model of Barabási and Albert [A. L. Barabási and R. Albert, Science 286, 509 (1999)] through the use of various Path finding strategies. In real networks, global network information is not accessible to each vertex, and the Actual Path connecting two vertices can sometimes be much longer than the shortest one. A generalized diameter depending on the Actual Path finding strategy is introduced, and a simple strategy, which utilizes only local information on the connectivity, is suggested and shown to yield small-world behavior: the diameter D of the network increases logarithmically with the network size N, the same as is found with global strategy. If Paths are sought at random, D is equivalent to N(0.5) is found.

Stefan Funke - One of the best experts on this subject based on the ideXlab platform.

  • COCOON - Seamless Interpolation Between Contraction Hierarchies and Hub Labels for Fast and Space-Efficient Shortest Path Queries in Road Networks
    Lecture Notes in Computer Science, 2020
    Co-Authors: Stefan Funke
    Abstract:

    We propose a conceptually simple, yet very effective extension of the highly popular Contraction Hierarchies (CH) speedup technique improving query times for shortest Paths in road networks by one order of magnitude with very modest space overhead. Using our scheme we are able to answer queries on continental-sized road networks with more than half a billion edges in the microseconds range on standard workstation hardware. Previous approaches that are considerably faster than CH were only for shortest Path distance queries (recovering the Actual Path required additional effort and space) or suffered from humongous space consumption hindering their practicality for large real-world road networks. Our approach can be interpreted as a seamless interpolation between Contraction Hierarchies and Hub Labels.